|
|||||
|
|
On the Commutativity of Weakly Commutative Riemannian Homogeneous Spaces |
|
| Authors: | L G Rybnikov |
| Institution: | (1) Department of Mechanics and Mathematics, Moscow State University, Russia |
| Abstract: | A Riemannian homogeneous space X=G/H is said to be commutative if the algebra of G-invariant differential operators on X is commutative and weakly commutative if the associated Poisson algebra is commutative. Clearly, the commutativity of X implies its weak commutativity. The converse implication is proved in this paper. |
| Keywords: | Lie group Lie algebra universal enveloping algebra homogeneous space (weakly) commutative space symplectic manifold Poisson bracket momentum map |
| 本文献已被 SpringerLink 等数据库收录！ | |